Equation 5 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
Fix the vocabulary first. Let N be total parameters, the parameters actually used to process a given token, D training tokens, and M the memory that must be resident to serve. For the dense decoder-only transformer that remains the default architecture [ 1 ] , = N and M N . Every method below breaks one of those two identities, and which one it breaks determines what it is good for.
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